Substantial effort has been drawn for years onto the development of (possibly high-order) numerical techniques for the scalar homogeneous conservation law, an equation which is strongly dissipative in L1 thanks to shock wave formation. Such a dissipation property is generally lost when considering hyperbolic systems of conservation laws, or simply inhomogeneous scalar balance laws involving accretive or space-dependent source terms, because of complex wave interactions. An overall weaker dissipation can reveal intrinsic numerical weaknesses through specific nonlinear mechanisms: Hugoniot...
Substantial effort has been drawn for years onto the development of (possibly high-order) numerical techniques for the scalar homogeneous conservation...
This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard,...
This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A...
This book book explores the ways that elaborate flux functions can be constructed, mainly in a one-dimensional context for hyperbolic systems admitting shock-type solutions and also for kinetic equations in the discrete-ordinate approximation.
This book book explores the ways that elaborate flux functions can be constructed, mainly in a one-dimensional context for hyperbolic systems admittin...
This volume gathers contributions reflecting topics presented during an INDAM workshop held in Rome in May 2016. The event brought together many prominent researchers in both Mathematical Analysis and Numerical Computing, the goal being to promote interdisciplinary collaborations. Accordingly, the following thematic areas were developed:
1. Lagrangian discretizations and wavefront tracking for synchronization models;
2. Astrophysics computations and post-Newtonian approximations;
3. Hyperbolic balance laws and corrugated isometric embeddings;
4. "Caseology"...
This volume gathers contributions reflecting topics presented during an INDAM workshop held in Rome in May 2016. The event brought together many pr...
